A closed-loop calibrated digital twin for vibration suppression and performance enhancement of the milking robot manipulator

The Automatic Milking System (AMS) has significantly improved dairy farming efficiency. However, residual vibrations generated by the high-speed motion of the milking manipulator continue to pose significant challenges, particularly by compromising positioning accuracy and cup attachment performance. This paper proposes a Closed-Loop Calibrated Digital Twin (CLCDT) framework to achieve low-cost, real-time vibration suppression. First, a dynamic model incorporating joint stiffness and damping is formulated using Lagrange mechanics. For online calibration, a Recursive Least Squares with Forgetting Factor (RLS-FF) method rapidly identifies these parameters within 18 iterations. A Deep Neural Network (DNN) surrogate model is then developed to predict residual vibration characteristics achieving dynamic response prediction errors of only 3.30% for dominant frequency and 5.54% for stabilization time. Finally, a differential evolution (DE) optimized AS-curve trajectory planner is integrated into the system. Experimental results show that compared to conventional T-type planning, the proposed method reduces residual vibration stabilization time to under 0.07 s (a maximum improvement of 57.33%). In practical cup-attachment tasks, total process time was reduced by an average of 0.52 s, and visual positioning time decreased by 48.78%. These findings validate that the CLCDT framework significantly enhances operational efficiency and accuracy.